Homework (HW): Module 2/3 Lesson 10 Problem Set

8•2/3 HW Lesson 10

HW.10

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1. Let there be a dilation from center 𝑂. Then, 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝑃) = 𝑃′ and 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝑄) = 𝑄′. Examine the drawing below.

What can you determine about the scale factor of the dilation?

2. Let there be a dilation from center 𝑂. Then, 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝑃) = 𝑃′, and 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝑄) = 𝑄′. Examine the drawing below.

What can you determine about the scale factor of the dilation?

Name _______________________________________ Date Due: __________ Period: _____

Homework (HW): Module 2/3 Lesson 10 Problem Set

8•2/3 HW Lesson 10

HW.10

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3. Let there be a dilation from center 𝑂 with a scale factor 𝑟 = 4. Then, 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝑃) = 𝑃′ and 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝑄) = 𝑄′.

|𝑂𝑃| = 3.2 cm, and |𝑂𝑄| = 2.7 cm, as shown. Use the drawing below to answer parts (a) and (b). The drawing is not

to scale (meaning you can’t measure to determine the answer).

a. Use the definition of dilation to determine |𝑂𝑃′|.

b. Use the definition of dilation to determine |𝑂𝑄′|.

4. Let there be a dilation from center 𝑂 with a scale factor 𝑟. Then, 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝐴) = 𝐴′, 𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝐵) = 𝐵′, and

𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛(𝐶) = 𝐶′. |𝑂𝐴| = 3, |𝑂𝐵| = 15, |𝑂𝐶| = 6, and |𝑂𝐵′| = 5, as shown. Use the drawing below to answer parts

(a)–(c).

a. Using the definition of dilation with lengths 𝑂𝐵 and 𝑂𝐵′, determine the scale factor of the dilation.

Homework (HW): Module 2/3 Lesson 10 Problem Set

8•2/3 HW Lesson 10

HW.10

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b. Use the definition of dilation to determine |𝑂𝐴′|.

c. Use the definition of dilation to determine |𝑂𝐶′|.

5. Use a ruler to dilate the following figure from center 𝑂, with scale factor 𝑟 =12

.

6. Use a compass to dilate the figure 𝐴𝐵𝐶𝐷𝐸 from center 𝑂, with scale factor 𝑟 = 2.

Homework (HW): Module 2/3 Lesson 10 Problem Set

8•2/3 HW Lesson 10

HW.10

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7. Given center 𝑂 and triangle 𝐴𝐵𝐶, dilate the figure from center 𝑂 by a scale factor of 𝑟 =14

. Label the dilated triangle

𝐴′𝐵′𝐶′.

8. A line segment 𝐴𝐵 undergoes a dilation. Based on today’s lesson, what is the image of the segment?

9. ∠𝐺𝐻𝐼 measues 78°. After a dilation, what is the measure of ∠𝐺′𝐻′𝐼′? How do you know?